Mathematical model for IL-2-based cancer immunotherapy.

A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD4+ T cells, the relative death rate of CD8+ T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD4+ T cells die out. However, in cases where CD4+ and CD8+ T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD4+ T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD4+ T cells, while high doses for a short period of time over several days transiently increase the population of CD8+ T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size.

A stochastic framework for evaluating CAR T cell therapy efficacy and variability.

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.

Stochastic dynamics of human papillomavirus delineates cervical cancer progression.

Starting from a deterministic model, we propose and study a stochastic model for human papillomavirus infection and cervical cancer progression. Our analysis shows that the chronic infection state as random variables which have the ergodic invariant probability measure is necessary for progression from infected cell population to cervical cancer cells. It is shown that small progression rate from infected cells to precancerous cells and small microenvironmental noises associated with the progression rate and viral infection help to establish such chronic infection states. It implicates that large environmental noises associated with viral infection and the progression rate in vivo can reduce chronic infection. We further show that there will be a cervical cancer if the noise associated with precancerous cell growth is large enough. In addition, comparable numerical studies for the deterministic model and stochastic model, together with Hopf bifurcations in both deterministic and stochastic systems, highlight our analytical results.

α-Lactalbumin Peptide Asp-Gln-Trp Ameliorates Hepatic Steatosis and Oxidative Stress in Free Fatty Acids-Treated HepG2 Cells and High-Fat Diet-Induced NAFLD Mice by Activating the PPARα Pathway.

SCOPE: Dietary intervention has emerged as a promising strategy for the management of nonalcoholic fatty liver disease (NAFLD). The aim of this study is to investigate the ameliorative effects of the α-lactalbumin peptide Asp-Gln-Trp (DQW) against NAFLD and the underlying mechanism. METHODS AND RESULTS: The models of lipid metabolism disorders are established both in HepG2 cells and in C57BL/6J mice. The results demonstrate that DQW activates peroxisome proliferator-activated receptor α (PPARα) and subsequently ameliorates lipid deposition and oxidative stress in vitro. Interestingly, GW6471 markedly attenuates the modulatory effects of DQW on the PPARα pathway in HepG2 cells. Moreover, results of in vivo experiments indicate that DQW alleviates body weight gain, dyslipidemia, hepatic steatosis, and oxidative stress in high-fat-diet (HFD)-induced NAFLD mice. At the molecular level, DQW activates PPARα, subsequently enhances fatty acid ß-oxidation, and reduces lipogenesis, thereby ameliorating hepatic steatosis. Meanwhile, DQW may ameliorate liver injury and oxidative stress via activating the PPARα/nuclear-factor erythroid 2 (Nrf2)/heme-oxygenase 1 (HO-1) pathway. CONCLUSION: Those results indicate that α-lactalbumin peptide DQW may be an effective dietary supplement for alleviating NAFLD by alleviating lipid deposition and oxidative stress.

Effects of ultrasound on the structural and functional properties of sheep bone collagen.

The study evaluated the effect of an ultrasound-assisted treatment on the structural and functional properties of sheep bone collagen (SBC). The type and distribution of SBC were analyzed by proteome (shotgun) technology combined with liquid chromatography-tandem mass spectrometry. Compared with pepsin extraction, the ultrasound-assisted treatment significantly increased the collagen extraction rate by 17.4 pp (P < 0.05). The characteristic functional groups and structural integrity of collagen extracted by both methods were determined via Fourier transform infrared spectroscopy, ultraviolet absorption spectroscopy, and fluorescence spectroscopy. Circular dichroism spectra revealed that the ultrasound-assisted pretreatment reduced α-helix content by 1.6 pp, ß-sheet content by 21.9 pp, and random coils content by 28.4 pp, whereas it increased ß-turn content by 51.9 pp (P < 0.05), compared with pepsin extraction. Moreover, ultrasound-assisted treatment collagen had superior functional properties (e.g., solubility, water absorption, and oil absorption capacity) and foaming and emulsion properties, compared with pepsin extraction. Furthermore, the relative content of type I collagen in ultrasound-assisted extracted SBC was highest at 79.66%; only small proportions of type II, VI, X, and XI collagen were present. Peptide activity analysis showed that SBC had potential antioxidant activity, dipeptidyl peptidase 4 inhibitory activity, and angiotensin-converting enzyme inhibitory activity; it also had anticancer, antihypertensive, anti-inflammatory, and immunomodulatory effects.

High Levels of Extracellular Potassium Can Delay Myxoma Virus Replication by Preventing Release of Virions from the Endosomes.

Potassium (K+) is one of the most abundant cations in the human body. Under normal conditions, the vast majority of K+ is found within cells, and the extracellular [K+] is tightly regulated to within 3.0 to 5.0 mM. However, it has recently been shown that high levels of localized necrosis can increase the extracellular concentration of K+ to above 50 mM. This raises the possibility that elevated extracellular K+ might influence a variety of biological processes that occur within regions of necrotic tissue. For example, K+ has been shown to play a central role in the replication cycles of numerous viral families, and in cases of lytic infection, localized regions containing large numbers of necrotic cells can be formed. Here, we show that the replication of the model poxvirus myxoma virus (MYXV) is delayed by elevated levels of extracellular K+. These increased K+ concentrations alter the cellular endocytic pathway, leading to increased phagocytosis but a loss of endosomal/lysosomal segregation. This slows the release of myxoma virus particles from the endosomes, resulting in delays in genome synthesis and infectious particle formation as well as reduced viral spread. Additionally, mathematical modeling predicts that the extracellular K+ concentrations required to impact myxoma virus replication can be reached in viral lesions under a variety of conditions. Taken together, these data suggest that the extracellular [K+] plays a role in determining the outcomes of myxoma infection and that this effect could be physiologically relevant during pathogenic infection. IMPORTANCE Intracellular K+ homeostasis has been shown to play a major role in the replication of numerous viral families. However, the potential impact of altered extracellular K+ concentrations is less well understood. Our work demonstrates that increased concentrations of extracellular K+ can delay the replication cycle of the model poxvirus MYXV by inhibiting virion release from the endosomes. Additionally, mathematical modeling predicts that the levels of extracellular K+ required to impact MYXV replication can likely be reached during pathogenic infection. These results suggest that localized viral infection can alter K+ homeostasis and that these alterations might directly affect viral pathogenesis.

Hopf bifurcation without parameters in deterministic and stochastic modeling of cancer virotherapy, part II.

In part II, we analyze our stochastic model which incorporates microenvironmental noises and uncertainties related to immune responses. Outcomes of the therapy in our model are largely determined by the infectivity constant, the infection value, and stochastic relative immune clearance rates. The infection value is a universal critical value for immune-free ergodic invariant probability measures and persistence in all cases. Asymptotic behaviors of the stochastic model are similar to those of its deterministic counterpart. Our stochastic model displays an interesting dynamical behavior, stochastic Hopf bifurcation without parameters, which is a new phenomenon. We perform numerical study to demonstrate how stochastic Hopf bifurcation without parameters occurs. In addition, we give biological implications about our analytical results in stochastic setting versus deterministic setting.

Drying methods influence the physicochemical and functional properties of seed-used pumpkin.

The effects of far-infrared radiation drying (FIRD), freeze drying (FD), vacuum drying (VD), and hot air drying (HAD) on appearance, physicochemical properties, antioxidant activities, antityrosinase capacity using B16F10 melanoma cell from seed-used pumpkins (hull-less pumpkin and hull pumpkin) were evaluated. Results suggested that hull-less pumpkin (HLP) dehydrated by FIRD provided the highest total polyphenols content (37.11 ± 1.05 mg GAE/ g DW) and the ability of scavenging free radicals. HPLC analysis exhibited that coumaric acid was predominant phenolic acid in pumpkin. The correlation analysis demonstrated that polyphenolic compounds were related to antioxidant capacity. HLP-FD possessed better colour, higher preservation of ß-carotene, ascorbic acid and higher sugar contents compared with HLP-HAD. The highest antityrosinase activity was recorded in HLP-VD with a concentration of 37.16%. The melanin inhibition increased to 76.61%, and intracellular tyrosinase activity in B16F10 melanoma cells decreased to 88.63% at 800 µg/mL of polyphenol extract.

Deterministic and stochastic modeling for PDGF-driven gliomas reveals a classification of gliomas.

Motivated by our study of infiltrating dynamics of immune cells into tumors, we propose a stochastic model in terms of Ito stochastic differential equations to study how two parameters, the chemoattractant production rate and the chemotactic coefficient, influence immune cell migration and how these parameters distinguish two types of gliomas. We conduct a detailed analysis of the stochastic model and its deterministic counterpart. The deterministic model can differentiate two types of gliomas according to the range of the chemoattractant production rate as two equilibrium solutions, while the stochastic model also can differentiate two types of gliomas according to the ranges of the chemoattractant production rate and chemotactic coefficient with thresholds as one non-zero ergodic invariant measure and one weak persistent state when the noise intensities are small. When the noise intensities are large comparing with the chemotactic coefficient, there is only one type of glioma that corresponds to a non-zero ergodic invariant measure. Using our experimental data, numerical simulations are carried out to demonstrate properties of our models, and we give medical interpretations and implications for our analytical results and numerical simulations. This study also confirms some of our results about IDH gliomas.

Effect of oil surface activity on oil absorption behavior of potato strips during frying process.

Oil absorption behavior of fried foods is affected by oil property during frying process. The present study investigated the effect of oil viscosity and surface activity on the oil uptake of fried potato strips with frying temperature. Results showed that oil content of palm oil (PO) and soybean oil (SBO) in fried strips increased with the frying temperature between 140 °C and 180 °C, while deceased at 200 °C. Oil distribution determined by LF-NMR and CLSM confirmed the changes of oil content of fried potato strips. Interfacial tension and surfactant content (monoglycerides, diglycerides, total polar compounds) of PO and SBO increased with frying temperature and affected the oil absorption of fried strips. Frying temperature and oil type showed no effect on surface tension. Besides, the higher level of viscosity, interfacial tension and surfactants of SBO than those of PO facilitated the more SO and TO of fried potato strips.

Relationship between crust characteristics and oil uptake of potato strips with hot-air pre-drying during frying process.

Crust property is an important factor in affecting the oil absorption of potato strips. The present study aimed at illustrating detailed crust characteristics in relation to oil uptake of potato strips during frying as a function of hot-air pre-drying time. Results showed that oil content decreased with the increasing hot-air pre-drying time. Oil distribution determined by LF-NMR and CLSM confirmed pre-drying could reduce oil uptake of potato strips. Structural and textural analysis of crust revealed the increase in crust ratio, roughness and texture (Fm, Nwr, fwr, Wc), and decrease in crust uniformity. Results of microscopic structure unraveled that the crust of fried strips after pre-drying for 180 min became thick and compact with almost no pores. Our results suggested that hot-air pre-drying caused the formation of harder and denser crust, and oil uptake of fried potato strips after pre-drying largely depended on crust texture rather than morphology.

Effects of frying temperature and pore profile on the oil absorption behavior of fried potato chips.

In present study, total oil (TO), surface oil (SO), structural oil (STO), penetrated surface oil (PSO), and oil distribution during frying were analyzed. Results showed STO (53.10-75.89%) fraction made up the largest part of TO followed by PSO (36.26-58.28%) and SO (2.59-3.50%), and the proportion of STO in TO decreased with the increasing frying time, while PSO elevated, indicating the higher frying temperature facilitated the formation of less and smaller pore in samples, and thus led to the less oil content. Therefore, effect of pore on oil absorption was further investigated. Results showed there was no significant difference in oil content of samples with initial pore diameter of 0-0.2 mm. While, TO (mainly STO) increased with the increasing initial pore diameter of 0.3-1.2 mm. The bigger initial pore diameter induced bigger pore volume and porosity. Taken together, this study provided new ideas to clarify oil absorption based on pore profiles.

Basic stochastic model for tumor virotherapy.

The complexity of oncolytic virotherapy arises from many factors. In this study, we incorporate environmental noise and stochastic effects to our basic deterministic model and propose a stochastic model for viral therapy in terms of Ito stochastic differential equations. We conduct a detailed analysis of the model using boundary methods. We find two combined parameters, one describes possibilities of eradicating tumors and one is an increasing function of the viral burst size, which serve as thresholds to classify asymptotical dynamics of the model solution paths. We show there are three ergodic invariant probability measures which correspond to equilibrium states of the deterministic model, and extra possibility to eradicate tumor due to strong variance of tumor growth rate and medium viral burst size. Numerical analysis demonstrates several typical solution paths with biological explanations. In addition, we provide some medical interpretations and implications.

Mathematical modeling of PDGF-driven glioma reveals the dynamics of immune cells infiltrating into tumors.

BACKGROUND: Tumor-infiltrated immune cells compose a significant component of many cancers. They have been observed to have contradictory impacts on tumors. Although the primary reasons for these observations remain elusive, it is important to understand how immune cells infiltrating into tumors is regulated. Recently our group conducted a series of experimental studies, which showed that muIDH1 gliomas have a significant global reduction of immune cells and suggested that the longer survival time of mice with CIMP gliomas may be due to the IDH mutation and its effect on reducing of the tumor-infiltrated immune cells. However, to comprehend how IDH1 mutants regulate infiltration of immune cells into gliomas and how they affect the aggressiveness of gliomas, it is necessary to integrate our experimental data into a dynamical system to acquire a much deeper understanding of subtle regulation of immune cell infiltration. METHODS: The method is integration of mathematical modeling and experiments. According to mass conservation laws and assumption that immune cells migrate into the tumor site along a chemotactic gradient field, a mathematical model is formulated. Parameters are estimated from our experiments. Numerical methods are developed to solve the problem. Numerical predictions are compared with experimental results. RESULTS: Our analysis shows that the net rate of increase of immune cells infiltrated into the tumor is approximately proportional to the 4/5 power of the chemoattractant production rate, and it is an increasing function of time while the percentage of immune cells infiltrated into the tumor is a decreasing function of time. Our model predicts that wtIDH1 mice will survive longer if the immune cells are blocked by reducing chemotactic coefficient. For more aggressive gliomas, our model shows that there is little difference in their survivals between wtIDH1 and muIDH1 tumors, and the percentage of immune cells infiltrated into the tumor is much lower. These predictions are verified by our experimental results. In addition, wtIDH1 and muIDH1 can be quantitatively distinguished by their chemoattractant production rates, and the chemotactic coefficient determines possibilities of immune cells migration along chemoattractant gradient fields. CONCLUSIONS: The chemoattractant gradient field produced by tumor cells may facilitate immune cells migration to the tumor cite. The chemoattractant production rate may be utilized to classify wtIDH1 and muIDH1 tumors. The dynamics of immune cells infiltrating into tumors is largely determined by tumor cell chemoattractant production rate and chemotactic coefficient.

Stochastic growth pattern of untreated human glioblastomas predicts the survival time for patients.

Glioblastomas are highly malignant brain tumors. Knowledge of growth rates and growth patterns is useful for understanding tumor biology and planning treatment logistics. Based on untreated human glioblastoma data collected in Trondheim, Norway, we first fit the average growth to a Gompertz curve, then find a best fitted white noise term for the growth rate variance. Combining these two fits, we obtain a new type of Gompertz diffusion dynamics, which is a stochastic differential equation (SDE). Newly collected untreated human glioblastoma data in Seattle, US, re-verify our model. Instead of growth curves predicted by deterministic models, our SDE model predicts a band with a center curve as the tumor size average and its width as the tumor size variance over time. Given the glioblastoma size in a patient, our model can predict the patient survival time with a prescribed probability. The survival time is approximately a normal random variable with simple formulas for its mean and variance in terms of tumor sizes. Our model can be applied to studies of tumor treatments. As a demonstration, we numerically investigate different protocols of surgical resection using our model and provide possible theoretical strategies.

Effects of Exogenous Synthetic Autoinducer-2 on Physiological Behaviors and Proteome of Lactic Acid Bacteria.

Bacterial populations use a cell-to-cell communication system to coordinate community-wide regulation processes, which is termed quorum sensing (QS). Autoinducer-2 (AI-2) is a universal signal molecule that mediates inter- and intraspecies QS systems among different bacteria. In this study, the effects of exogenous addition of AI-2 synthesized in vitro on physiological behaviors and proteome were investigated in lactic acid bacteria strains. Exogenous AI-2 had a concentration-dependent effect on the Enterococcus faecium 8-3 cell density. There was no significant influence on biofilm formation and individual morphology of cells upon 60 µM AI-2 addition in E. faecium 8-3 and Lactobacillus fermentum 2-1. However, it improved the acid and alkali resistance of E. faecium 8-3. With the addition of AI-2, 15 differentially expressed proteins were identified in E. faecium 8-3, which participate in RNA transport signaling, RNA polymerase, ribosome, oxidative phosphorylation, cysteine and methionine metabolism, pyrimidine metabolism, ATP-binding cassette (ABC) transporters, purine metabolism, biosynthesis of the amino acid pathway, etc. Among them, the expression of 5-methylthioadenosine/S-adenosylhomocysteine nucleosidase, which is known to be involved in AI-2 synthesis and cysteine and amino acid metabolism, was upregulated. These findings will lay the foundation to clarify the mechanism of cell-to-cell communication and bacterial physiological behaviors mediated by AI-2.

Backward Hopf bifurcation in a mathematical model for oncolytic virotherapy with the infection delay and innate immune effects.

In this paper, we consider a system of delay differential equations that models the oncolytic virotherapy on solid tumours with the delay of viral infection in the presence of the innate immune response. We conduct qualitative and numerical analysis, and provide possible medical implications for our results. The system has four equilibrium solutions. Fixed point analysis indicates that increasing the burst size and infection rate of the viruses has positive contribution to the therapy. However, increasing the immune killing infection rate, the immune stimulation rate, or the immune killing virus rate may lead the treatment failed. The viral infection time delay induces backward Hopf bifurcations, which means that the therapy may fail before time delay increases passing through a Hopf bifurcation. The parameter analysis also shows how saddle-node and Hopf bifurcations occur as viral burst size and other parameters vary, which yields further insights into the dynamics of the virotherapy.

Spatial Model for Oncolytic Virotherapy with Lytic Cycle Delay.

We formulate a mathematical model of functional partial differential equations for oncolytic virotherapy which incorporates virus diffusivity, tumor cell diffusion, and the viral lytic cycle based on a basic oncolytic virus dynamics model. We conduct a detailed analysis for the dynamics of the model and carry out numerical simulations to demonstrate our analytic results. Particularly, we establish the positive invariant domain for the [Formula: see text] limit set of the system and show that the model has three spatially homogenous equilibriums solutions. We prove that the spatially uniform virus-free steady state is globally asymptotically stable for any viral lytic period delay and diffusion coefficients of tumor cells and viruses when the viral burst size is smaller than a critical value. We obtain the conditions, for example the ratio of virus diffusion coefficient to that of tumor cells is greater than a value and the viral lytic cycle, is greater than a critical value, under which the spatially uniform positive steady state is locally asymptotically stable. We also obtain conditions under which the system undergoes Hopf bifurcations, and stable periodic solutions occur. We point out medical implications of our results which are difficult to obtain from models without combining diffusive properties of viruses and tumor cells with viral lytic cycles.

E2F8 confers cisplatin resistance to ER+ breast cancer cells via transcriptionally activating MASTL.

MASTL (microtubule-associated serine/threonine kinase-like) is a critical kinase modulating mitotic entry. In this study, we investigated the mechanism of its dysregulation in breast cancer and its involvement in cisplatin resistance in ER+ breast cancer cells. Data mining in Kaplan-Meier Plotter showed that high MASTL expression was associated with worse distant metastasis free survival (DMFS) and relapse free survival (RFS) in ER+ breast cancer patients. In TCGA breast cancer cohort (TCGA-BRCA), MASTL was strongly co-upregulated with E2F8. High E2F8 expression was also strongly associated with unfavorable DMFS and RFS in ER+ breast cancer patients. Promoter scanning in JASPAR Database showed that the MASTL promoter region has a highly possible E2F8 binding site upstream the TSS site. The following western blot, dual luciferase assay and ChIP-qPCR validated this binding site. In MCF-7 cells, E2F8 overexpression alleviated cisplatin induced cell apoptosis by shortening G2/M arrest and promoting mitotic entry, the effect of which was largely canceled by inhibiting MASTL. Therefore, we infer that E2F8 can shorten cisplatin induced G2/M arrest by promoting MASTL mediated mitotic progression in ER+ breast cancer cells. These findings might help to explain why high MASTL or high E2F8 expression is associated with worse RFS in ER+ breast cancer.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.